Electrical computing instrument



Aug 26, 1952 D. F. WALKER 2,608,345

ELECTRICAL COMPUTING INSTRUMENT Filed May 19, 1948 2 SHEETS,-SHEET 1Mvenfir Damn WA]. KER

Aug. 26, 1952 D WALKER 2,608,345

ELECTRICAL COMPUTING INSTRUMENT Filed May 19, 1948 2 SHEETS-SHEET 2F/GZ.

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Patented Aug. 26, 1952 ELECTRICAL COMPUTING INSTRUMENT Donald F. Walker,Hollinwood, England, assigncr to Ferranti Limited, Hollinwood, England,a

British company pplicati n M y 1 1948, Serial No. 27,990

In Great Britain May 21, 1947 This invention relates to electricalcomputing instruments of the kind adapted for indicating or deriving thevalue of an unknown quantity of a problem to be solved from three knownquantities where the latter quantities are capable of being representedby suflicient information of the lengths of sides or values of angles todetermine a triangle uniquely, the unknown quantity being one of thedata not supplied, i. e. the length of a side or the value of an angle.Such problems are of frequent occurrence in connection with artillerypredictors, navigational computers, and the like. V

A particular example of such a problem arises in the case of radionavigational systems of the kind Where the information received by thecraft is in the form of (l) a time interval between signals radiatedfrom a master station and a slave station, these two stations beingfixed and their locations known, and (2) the bearing at the craft of themaster station. As will be shown in more detail hereinafter there may bederived from this information data that may be represented by (a) thelength of a first side of a triangle, (1)) the length-which may bepositive or negativeobtained by subtracting the length of the secondside from the length of the third side, and (c) the value of the anglebetween the first and second side's, theunknown quantity being thelength of the second side.

It is of course possible to draw a triangle from the data supplied andby measuring the appropriate side or angle determine the unknownquantity; but this procedure is often inconvenient to apply, especiallywhen the known quantities are continuously changing.

The main object of the present invention, therefore, is to provide anelectrical instrument of the kind above defined for automatically andcontinuously deriving the unknown quantity for visible indicationthereof or for application to a further computer, stage.

i In the accompanying drawings:

Figure 1 is a diagram to illustrate the principle of the invention,

Figure 2 is a circuit diagram to illustrate one embodiment of theinvention,

Figures 3 to 6 are circuit diagrams to illustrate modifications of theembodiment shown in Figure 2, i

Figure 7 is a circuit diagram to illustrate another embodiment of theinvention,

Figure 8 is a circuit diagram to illustrate a modification of any of theabove embodiments.

In carrying out the invention according to one 10 Claims. (01. 235-61)form by way of example, an aircraft at Psee Figure 1receivesnavigational information in the form of pulse signals radiated from afixed master station R and its fixed associated slave station Q. Pulsesare transmitted cyclically from these stations, each cycle comprising apulse transmitted from the master station followed by a pulsetransmitted from the slave station; the timeinterval between each suchpair of pulses is very accurately adjusted to a constant known value,i==[ The pair of pulses of each cycle is received by equipment on theaircraft and displayed on a cathode ray tube screen so that the timeinterval between the reception of the pulses may be accuratelydetermined. This time interval is clearly dependent on the differencebetween the distances of the stations from the aircraft.

Theaircraft is additionally provided with direction-finding equipmentdesigned to cooperate with a rotating beam radio beam located at themaster station and operating on the well-known omni-directional radiorange principle. The hearing at the aircraft of the master station isthereby readily ascertainable.

The electrical computing instrument in accordance with the inventionprovides from the foregoing pulse and bearing information received inthe aircraft an immediate indication at any instant of the aircraftsdistance from the master station R, thus simplifying and acceleratingthe ascertainment of the aircrafts position. The instrument, in effect,solves the triangle PQR when the following information is set into it,the geometrical convention being observed of referring to the angles ofthe triangle by the capital letters P, Q and R and the sides oppositethese angles by the lower case letters 20, q and 1' respectively: (a).the length of the first side 2 (b) the difference obtained bysubtracting the length of the second side q from the length of the thirdside ni. e. (r -q) and .(c) the value of the angle R between the firstand second sides p and q. Item (a) is constant and is known. Item (1))is obtained from the pulse receiving equipment carried by the aircraft,the cathode ray tube screen of which is calibrated to provide thisinformation direct from the spacing of the pulses along a horizontaltime-base. Item (0) is ob-- tained from the direction-finding equipment,also carried by. theaircraft. The unknown quantity derived by theinstrument is the length of the secondside q, i. e. the distance of theaircraft from the master station R. i In carrying out the invention,therefore, ac

cording to one form with reference to Figure 2 an electrical computinginstrument consists of a uniform resistor l having a mid-point 2 and avariable tapping 3 adjustable by a control 3 This control 3 has apointer arranged to traverse a dial calibrated in terms of thedifference length (r-q) in correspondence with the time-basecalibrations of the cathode ray tube of the pulsereceiving equipmentabove referred to. The dial calibrations are so related to the positionof tapping 3 that for each setting of control 3 the resistance betweentapping 3 and mid-point 2 of resistor i represents to a convenient scalethat value of the clifierence length (rq) indicated by the dial. Twofixed points 4, 5 on this resistor symmetrically disposed with respectto'midpoint 2, i. e. so that the resistance between points 2 and 4 isequal to that between points 2 and 5, are connected to a common lead 6by Way of equal first and second impedance means in the form of equalfixed resistors I and 8 respectively. It will be seen that theresistances of the two parallel paths between mid-point 2 and commonlead 6 by way of resistors 'l and 8 respectively are equal.

The value of each of these resistances is such as to represent the knownconstant length of the first side p to the same scale as that by whichthe resistance between tapping 3 and mid-point 2 represents thedifference length (rq) A source 9 of A. C. electrical energy isconnected across tapping 3 and common lead 6. point tapping It of a 1:1reversing auto-transformer H is connected to common lead 6; theprimarylead i2 is connected to the end of resistor 'l'remote from lead eand the secondary I3 is connected by way of cosine potentiometer M,having a variable tapping l5 adjustable by a control to the end ofresistor 8 remote from lead {5. Potentiometer is operates according to acosine law with respect to its mid-point l5, ipe. linear movement oftapping l5 in proportion to the value of a given angle 0 alters theresistance between tapping l5 and mid-point :6 in proportion to cos 6;when 0 is 90 degrees the tapping is at midpoint it; the transformer endof potentiometer I4 corresponds to 180 degrees and the other end to zerodegrees. Between tapping l5 and common lead 6 is connected a linearvariable potentiometer ll havin a variable tapping l8, adjustableby acontrol H5 connected by Way of the primary 59 of a control transformerto a tapping 2i on a fixed potentiometer 22 connected across the supply9. The output from the secondary 23 of the transformer 20, afteramplification by amplifier 24, is applied to a servomotor 25 thatoperates control I8 to adjust the position of tapping is ofpotentiometer H by means of a suitable drive indicated by 26, in amanner that will be made clearer hereinafter. Controls 3 and til may bedescribed as pre-set, that is to say operated by hand or by apparatusother than the computing instrument itself, as distinct from control it,which is operated by servomotor 25 forming part of that instrument.

In operation the navigator of the aircraft continually adjusts pre-setcontrol 3 so that the value of (r-q) indicated by the dial correspondsto that indicated on the cathode ray tube. Tapping l5 of cosinepotentiometer i4 is similarly maintained by means of pre-set control I5so that the angle 9 corresponds to the angle R, the voltage betweentapping l5 and mid-point l5 being therefore proportional to cos B. Thisangle is determined by a simple subtraction process from the bearing ofmaster station R at the air- The midcraft, as ascertained by thedirection finding equipment above referred to, and the known constantbearing at master station R of slave station Q. As is demonstratedbelow, the difference voltage applied to potentiometer H i. e. thevoltage between tapping l5 and common lead 6, is proportional to thereciprocal of the length of the unknown second side. The combination ofthe linear and fixed potentiometers H and'22 serves to invert thisreciprocal, as will be made clear later, so that when the resultant, i.e. the output, voltage of potentiometer I! is balanced by the outputvoltage of fixed potentiometer 22, in other words when the voltagebetween tapping l8 and common lead 6 is balanced by the voltage betweentapping 2| and common lead 6, the position of tapping its relative tocommon lead 6 is in conformity with the triangle representing the knownquantities, and so is proportional to the length of side q, whichlength, or the quantity it represents, may be read cit on a linear scaleadjacent to control 8 When these voltages are not equal an outof-balance current flows in transformer 26; the amplified secondaryvoltage then operates servomotor 25, which adjusts tapping [8 (throughcontrol i8 and drive 26) in such a direction as to bring the outputvoltages into balance; when this is attained the out-of-balance currentceases to fiow and motor 25 ceases to operate. This adjusting proceduremay occur continuously, controls 3 and I5 being continuously adjusted bythe navigator whilst control I8 is continuously adjusted in responsethereto, as above described, by the apparatus in accord ance with theinvention, thus giving a continuous indication of the value of q.

The operation of the above equipment will be madeclearer by thefollowing theoretical explanation.

A standard trigonometrical formula for the triangle PQR is As we aregiven (rq) we may substitute (q+rq) for 1':

Hence (q-|-r-q) :p +q -2pq cos R, from which may be derived theequation:

1 l-l-cosR 1cosR q z q) p+( q) Reverting now to the apparatus abovedescribed, as already stated the resistance between mid-point 2 ofresistance I and common lead 6 by way of either of fixed resistances lor 8 represents the length of side p. When the resistance betweentapping 3 and mid-point 2 is proportional to (r-q) as above described,the resistances of the two parallel paths between tapping 3 and commonlead 6 become p+ (rq) and p(rq). Using the suffix 1 when referring tothe parallel path between tapping 3 and common lead 5 by way of point 4and resistance 7 and the suffix 2 when referring to the other parallelpath we get for the currents i1 and is in the two paths:

i1 and i oc sistances I and B are equal. Voltage m is reversed inpolarity by reversing transformer H so that it is the sum of voltages inand 1);, rather than the difference, that is appliedto cosinepotentiometer [4. The voltage developed between tapping l5 and mid-pointl6 of this potentiometer is therefore proportional to /2(1J1+'l)2) cos6, and the voltage between tapping l5 and the end of potentiometer I4connected to resistance 8 (it is assumed for the moment that the valueof lies between 0 and 90 degrees) is proportional to The voltage givenin (4) subtracted from 122 is thus the diiference voltage (in, say)between tapping l5 and common lead 6. Hence:

On substituting for v1 and 122 the values from (3) to which i1 and i2are proportional and substitutlng R for 0 we get:

1+cos R l-cos R p-( a) p+( q) (6) The difference voltage '03 mayalternatively be derived from the voltage between tapping l5 and the endof potentiometer [4 connected to autotransformer secondary 13 less thevoltage across this secondary. We then get:

from which expression (6.) may again be obtained.

Hence, from expression (2),

The setting of tapping 18 relative to common lead 6, as indicated bycontrol I8 is thus proportional to the length q required and hence tothe result of the computation. The tapping 2| on fixed potentiometer 22to give the fixed fraction it is chosen so as to allow of a convenientrange of adjustment of tapping [8.

When R is between 90 and 180 degrees, tapping l5 of cosine potentiometer14 operates on the other side of mid-point [6. The term (1cos R) inexpression (4) (with R substituted foro) becomes (1+cos R), cos B itselfbeing now a negative term.

Similarly when the length of side q is greater than the length of side 1tapping 3 of resistance I operates on the other side of mid-point 2. The

ranged so that the wanted base angle is the base angle R. The equalresistances between midpoint 2' and common lead 6 are made to correspondto the constant length of the side 12 and the drive 26 is connected tocontrol I5 instead of to control I8 Controls 3 and I8 arethen adjustedby hand, or automatically by some as sociated apparatus, to representthe length. (r-q) and the length q respectively, whilst motor 25maintains control l5 in conformity with the triangle representing theproblem, i. e. so that the angle 0 becomes angle R and may be read offfrom the scale associated with control I5 If the known quantities aresuch as may be represented by the fixed base p, the side q and theincluded angle R, the unkonwn quantity being the side 1", controls l5and I8 are adjusted to represent R and q respectively whilst the motormaintains control 3 in conformity. Th answer derived from the positionof control 3 will be (rq), from which the value of 1 may be obtained byadding the known quantity q, e. g. by means of a differential gear.

In any of the above-described embodiments resistances 1 and 8 may bereplaced by chokes designed to yield voltages proportional to thecurrents flowing through them. This is illustrated in Figure 3, whichshows only the pertinent portion of Figure 2, 21 and 28 being the chokessubstituted for resistances l and 8 respectively.

In the above described embodiments, or as modified in the precedingparagraph, it is assumed that the voltages in and v2 across theimpedances between uniform resistance 1 and common lead 6 are entirelydue to the currents i1 and is set up by the supply voltage. In practicehowever voltage in across the impedance which is included in thesecondary circuit of 1:1 transformer It is to some extent effected bythe local current set up in this circuit by transformeraction and henceby i1. Similarly the current in the primary circuit, and hence in isaffected by 712. To eliminate or reduce the errors that result from thisa correcting winding 60 (see Figure 4) is added to transformer ll. Oneend of winding 60 is connected to common lead 6 and the other end isconnected by way of a variable resistance 6| to fixed point 5. Winding60 is connected in such a sense that it sets up currents in the primaryand secondary circuits which by adjustment of variable resistance 6| maybe made to balance out the undesired currents in these circuits.

In an alternative arrangement for eliminating or reducing these errors,illustrated in Figure 5, a resistance 10 may be connected acrossresistance I having a value equal to that of cosine potentiometer I4,thus causing neutralizing currents to be set up in a similar manner.

The irnpedances between the uniform resistance l and the common lead. 6may alternatively take the form of primaries 50 and 5| (see Figure 6) oftransformers 52 and 53 of equal ratio, the secondaries 54 and 55 ofwhich are connected as shown to cosine potentiometer Hi. It will beappreciated that in this embodiment the 1:1 transformer H is notnecessary, the required voltage reversal to produce (vi-Hm) beingeffected by reversing the connections to one of the secondaries.

Another embodiment of the invention is illustrated in Figure 7. In thisthe two fixed resistances 1 and 8 are replaced by two equal-resistancecosine potentiometers 30 and 3| respectively, each covering the range0-180 and having tappings 32 and 33 respectively. The potentiometersareoppositelydisposed'so that the 'zero angle end of potentiometer 30 isconnectedto common lead 6. but thezero angle end of potentimeter BI isconnectedtoresistance I; Tappings 32 and 33 are ganged to be moved'inopposite directions by acontrol. 34 so that the positions or" the twotappings are always appropriate to the same angle the cosine of which isproportional to the distance of each tapping from the mid-point of theassociated potentiometer; these two tappings arethus always onoppositesides-of mid-points 35,36 with respect to common lead 6. Tappings 32 and33 are-connected together by way of the primary-Hot a transformer 38,the secondary 39 of which is connected across potentiometer H by wayofcommonlead 6. The cosine-potentiometer I4 and transformer l l of theembodiment described with reference to Figure 1 are omitted but; theother items of. equipment remain the same. 7

The. operation of the instrumentis exactly as described in the saidembodiment except that control 34 is now adjustedinstead of control I InFigure 7, control 34 is shown as being. adjusted by motor (through drive26), thus illustrating the use of the instrument for the solution ofthat typev of problem where the angle R is unknown and isto befound; butit will'of course be understood that this embodimentmay also be used asin the said embodiment forthesolution of those types of problemswherethe. angleR is known and the control 34 is accordingly set by hand orby. the associated apparatus.

The theoretical explanation of the principle of operation of thisembodiment is as follows. From the. foregoing description it will beseen that the outputpotential between tapping 32 of potentiometer andcommon lead 6 is proportional to (l.cos .0)v1 and the output potentialbetween tapping 33 of potentiometer 3| and common lead Gpropo'rtional to(l+cos 0) on, where 6 is the angle to whichcontrol 34 is adjusted and v1and mare the. respective potentials developed across the potentiometer.When the position of contrcl3l is. in conformity with the triangle PQR"we can substitute R for 0; the voltage applied to potentiometer. I? is.therefore proportionalto the'difference between these output potentialsi. e.

substituting the usual values of 2'1 and is to which.

111 and '02 arev proportional (see expression (3) above) we get:

opposite directions thereby maintaining the re-v sistance betweenmid-point 2 and tappingdfl always equal to the resistance between mid-point land tapping-41; Control 42 may be adjusted by the motor if thelength of the base 17 is the unknown quantity to be found; otherwise itmay beadjusted by hand or by the associated apparatus. This modificationclearly extends therange of problems thatthe. instrument can solve. For

instance, if the known quantities are such as may be'represented by allthree sides of atriangle, all

threesides maybe continuously variable instead of one having to befixed; and solutions may be obtained-when the three known quantities aresuch as may be represented by two sides and the.

The cosine potentiometers as used in theiabove.

embodiments may comprise resistances Wound according to a cosine law andhaving slides moving uniformly, or uniformly wound resistances havingslides moving in accordance with a cosinelaw;

It is to be-understood that the apparatus above described may bemodified in many respects without departing from the invention. Withslight modification of the equipment sine potentiometers may forinstance be used instead of cosine. The means for'deriving theout-of-balancecurrent may also be modified; the voltage directlyproportional to the source 9 of electrical energy may in Figure 2 beapplied direct to tapping l8, the primary I9 being. included in the leadfrom potentiometer i! to tapping 15.

As. the apparatus workson thenull balance. principle the supply voltageneed not be constant but may with advantage bevaried so as not tooverload any part of the apparatus when one or more of the sliders isoperating near an extreme position on the associated resistance orpotentiometer.

In any of the above described embodiments the control adjusted by the,motor may alternatively be applied to a further: computer stage.

I claim:

1. An electrical computing instrument, for deriving the value ofail-unknown quantity of a problem to be solved from three knownquantities I difference between said voltage 112 and a voltage of value(v1+vz) (l cos 0), said means including a secondcontrol, the angle 0being represented by the position of said second control, a linear po--tent ometer having a variable tapping which de-- rlves an output voltageproportional to the said difference voltage, reference voltage-meansconnected with said source and providing a reference voltage,out-of-balance current means-connected between the lastmentioned'variable tapping and said reference voltage means therebyderiving out-of-balance from the difference between saidoutputvoltageand said reference voltage, a third control associated with the saidvariable tapping of said linear potentiometer and theposition of whichthird control directly determines the valueofsaid out-of-balancecurrent, a motor actuated b Said out-ofe'balancecurrent and serving toad- Just one of said controls when the other two of said controlsarepre-set, in order to, bring the. quantity represented by thepositionofthe motor;-

adjusted control into conformity with the triangle representing saidknown quantities,

2. An electrical computing instrument as claimed in claim 1 wherein eachof said impedance means comprises a resistance.

3. An electrical computing instrument as claimed in claim 1 wherein eachof said impedance means comprises a choke.

4. An electrical computing instrument as claimed in claim 1 wherein saidimpedance means comprise transformers the primaries of which areconnected between said common lead and the appropriate ones of said twopoints and the secondaries of which are connected across opposite endsof said cosine potentiometer and said common lead.

5. An instrument as claimed in claim 1 wherein said means for deriving adifference voltage includes means for applying a voltage proportional to(m-H22) to a cosine potentiometer and the latter has a variable tappingcontrolled by said second control and said linear potentiometer isconnected between said cosine potentiometer and said conductor element.

6. An electrical computing instrument as claimed in claim 1 wherein saidfirst and second impedance means are constituted by two oppositelydisposed cosine potentiometers of equal resistance connecting saidconductor element to said two connecting points respectively, and saidmeans for deriving a difference voltage includes variable tappings forsaid potentiometers respectively, ganging means whereby said variabletappings are ganged so as to be moved in opposite directions, saidsecond control actuating said ganging means thereby yielding between onesaid ganged variable tapping and said conductor element a potentialproportional to (1-cos v1, and between the other said ganged variabletapping and said conductor element a potential proportional to (1+cos0W2.

7. An electrical computing instrument as claimed in claim 1, said meansfor deriving the clifierence voltage including means for applying avoltage proportional to (vi-H22) to said cosine potentiometer, said lastmentioned means including a reversing transformer.

8. An electrical computing instrument as tentiometer, means including areversing transformer for applying a voltage proportional to (UH-'02) toa cosine potentiometer, neutralizing means to counteract any undesiredcurrents inductively set up by said reversing transformer, saidneutralizing means comprisin an additional secondary winding on saidreversing transformer, the output of said additional winding beingadapted to be variably applied between one of said two points and saidcommon lead.

9. An electrical computing instrument as claimed in claim 1 wherein saidfirst and second impedance means are constituted by two oppositelydisposed cosine potentiometers of equal resistance connecting saidconductor element to said two connecting points respectively, and saidmeans for deriving a diiference voltage includes variable tapping forsaid potentiometers respectively, ganging means whereby said variabletappings are ganged so as to be moved in opposite directions, saidsecond control actuating said ganging means thereby yielding between onsaid ganged variable tapping and said conductor element an outputpotential proportional to (1-cos am, and between the other said gangedvariable tapping and said conductor element an output potentialproportional to (l-l-cos mm, and said means for providing an outputvoltage includes a transformer, the primary of which is connectedbetween said ganged variable tappings and the secondary of which isconnected to said linear potentiometer third control.

10. An electrical computing instrument as claimed in claim 1 whereinsaid connecting points are in the form of variable tappings and a fourthcontrol is provided and means whereby said last mentioned tappings areganged under said fourth control to move in opposite directions whilremaining symmetrically disposed with respect to the said mid-point.

DONALD F. WALKER.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 2,066,949 Ruiz Jan. 5, 19372,438,112 Darlington Mar. 23, 1948 2,439,381 Darlington Apr. 13, 19482,444,933 Jasperson July 13, 1948

